Name: couple moments and the right-hand rule
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 21 s
Channel: JoVE

Consider equal and parallel forces applied to rotate a ship&#39;s steering wheel. They are oppositely directed and create a couple moment that rotates the wheel in an anticlockwise direction.
The right-hand rule can be used to determine the direction of the couple moment. When the fingers are curled along the rotation direction, the thumb indicates the moment direction. It always acts perpendicular to the plane of the two forces.
In scalar formulation, the couple moment equals the force magnitude multiplied by the perpendicular distance between the forces.
In vector formulation, the couple moment of one of the forces about any point on its line of action equals zero. The moment of another force about this point equals the cross product of the position vector from the line of action of one force to the other and the applied force.
Consider two couple moments acting on a speed-reducer unit. Since each is a free vector, their resultant can be estimated by vector addition.
If there are more than two couple moments, this expression can be generalized.

couples: scalar and vector formulation

One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel&#39;s rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment. To apply this rule, one simply curls the fingers of their right hand along the direction of rotation. The thumb then points in the direction of the moment. It should be noted that the couple moment always acts perpendicular to the plane of the two forces.
In scalar formulation, the magnitude of the couple moment equals the force magnitude multiplied by the perpendicular distance between the forces. This relationship allows for quantifying the rotational effect of the applied forces.
In vector formulation, the couple moment of one of the forces about any point on its line of action equals zero. This is because the force and position vector are parallel, resulting in a zero cross-product. The moment of the other force about this point, however, equals the cross product of the position vector from the line of action of one force to the other and the applied force. This formulation offers a more comprehensive understanding of the couple moment&#39;s behavior concerning the applied forces and their positions.

Couples: Scalar and Vector Formulation

One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of ...

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couple moments and the right-hand rule

Couple moments describe the turning effect of two parallel forces that are equal in magnitude and opposite in sense. This force pair creates rotation instead of straight-line motion. A common example is a ship’s steering wheel, where a small turn can guide the ship through the ocean.

A couple moment can rotate clockwise or anticlockwise. The right-hand rule helps identify its direction. To use it, curl the fingers of your right hand in the direction of rotation. Your thumb points in the direction of the moment, which acts perpendicular to the plane of the two forces.

In scalar form, the magnitude of a couple moment is the force magnitude multiplied by the perpendicular distance between the forces. This gives a simple way to measure the rotational effect. In vector form, the moment of one force about any point on its line of action is zero because the force vector and position vector are parallel. The other force then produces a moment equal to the cross product of the position vector between the forces and the applied force.

Couple Moments and the Right-Hand Rule

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A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push. This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m). A common example is tightening a bolt with a lug wrench. In...

Couple moments describe the turning effect of two parallel forces that are equal in magnitude and opposite in sense. This force pair creates rotation instead of straight-line motion. A common example is a ship’s steering wheel, where a small turn can guide the ship through the ocean. A couple moment can rotate clockwise or anticlockwise. The right-hand rule helps identify its direction. To use it, curl the fingers of your right hand in the direction of rotation. Your thumb points in the...

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key terms and concepts

Learn how two equal and opposite forces create a couple moment, how the right-hand rule shows its direction, and how scalar and vector forms differ.

Couple Moments and the Right-Hand Rule | JoVE K12

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Couple Moments and the Right-Hand Rule

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